What is the derivative of f(x)=-4/3 x^{-5/2} ?

The derivative of f(x)=-4/3 x^{-5/2} is (10)/(3x^{7/2)}

What is the first derivative of f(x)=-4/3 x^{-5/2} ?

The first derivative of f(x)=-4/3 x^{-5/2} is (10)/(3x^{7/2)}

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derivative of

f (x) = - \frac{4}{3} x^{- \frac{5}{2}}

\frac{10}{3 x ^{\frac{7}{2}}}

Solution steps

\frac{d}{d x} (- \frac{4}{3} x^{- \frac{5}{2}})

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= - \frac{4}{3} \frac{d}{d x} (x^{- \frac{5}{2}})

Apply the Power Rule:

\frac{d}{d x} (x^{a}) = a \cdot x^{a - 1}

= - \frac{4}{3} (- \frac{5}{2} x^{- \frac{5}{2} - 1})

Simplify

- \frac{4}{3} (- \frac{5}{2} x^{- \frac{5}{2} - 1}) : \frac{10}{3 x ^{\frac{7}{2}}}

= \frac{10}{3 x ^{\frac{7}{2}}}

What is the derivative of f(x)=-4/3 x^{-5/2} ?
The derivative of f(x)=-4/3 x^{-5/2} is (10)/(3x^{7/2)}
What is the first derivative of f(x)=-4/3 x^{-5/2} ?
The first derivative of f(x)=-4/3 x^{-5/2} is (10)/(3x^{7/2)}